Generalized multivariate Pade approximants

A new definition of multivariate Pade approximation is introduced, which is a natural generalization of the univariate Pade approximation and consists in replacing the exact interpolation problem by a least squares interpolation. This new definition allows a straightforward extension of the Montessus de Ballore theorem to the multivariate case. Except for the particular case of the so-called homogeneous Pade approximants, this extension has up to now been impossible to obtain in the classical formulation of the multivariate Padi approximation. Besides, the least squares formulation can also be applied to the univariate case, and provides an alternative to the classical Pade interpolation. (C) 1998 Academic Press.